Question

P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.

• A. $x-7y-3=0$
• B. $2x-7y+3=0$
• C. $2x-7y-3=0$
• D. $2x+7y-3=0$

Answer 1

The correct option is C

$2x-7y-3=0$

The vertices of $\Delta PQR$ are P(3, 4), Q(7, -2) and R(-2, -1)
Let S be the mid-point of PQ, then RS is the median through R

$\therefore$ Coordinates of S are
$(\frac{3+7}{2},\frac{4-2}{2})=(5,1)$
Slope of RS, $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-1)}{5-(-2)}=\frac{2}{7}$
$\therefore$ The equation of the median RS is
$y-y_1=m(x-x_1)$
$\Rightarrow y-(-1)=\frac{2}{7}(x+2)$
$\Rightarrow y+1=\frac{2}{7}(x+2)$
$\Rightarrow 7y+7=2x+4$
$\Rightarrow 2x-7y-3=0$
Hence, the equation of the median of the triangle through R is $2x-7y-3=0$